Some info has stated that he left without his phone or that calls don't go through, but I'm puzzled with the picture of him seemingly holding up something on the bridge. It really looks like he's holding up a phone to take a picture.
I believe I've been on that AMTRAK route before. It's tons of commuters and you can really end up lost in all the people, especially once you get to Penn. Obviously, the first thought many would have is "How could nobody notice him traveling with just a backpack?" Lots of students go back and forth on that route (I'm assuming Keystone) and it wouldn't be anything strange. He would easily look like a kid coming back from home on a Sunday night.
About the Brooklyn Bridge: the Manhattan side has a lot of surveillance, but the Brooklyn side doesn't have as much. Still, plenty of bodegas and traffic cams must have caught him if he did indeed cross the bridge.
This is entirely speculation, but I wonder if he planned to disappear, that he would have planned around the snowstorm. That could be a way to help obscure his whereabouts.